Stable Model Reduction for Time‐Domain Room Acoustics: A Structure‐Preserving Formulation for Complex Boundaries
Abstract
ABSTRACT This work presents novel structure‐preserving formulations for stable model order reduction in the context of time‐domain room acoustics simulations. A solution to address the instability in conventional model order reduction formulations based on the Linearized Euler Equations is derived and validated through numerical experiments. For the scenarios presented, the proposed formulation demonstrates 3.5 times speedup in calculating the full‐order model compared to the unstable formulation. A critical stability analysis is performed to identify the eigenvalues of the reduced operator matrices falling on the right half of complex plane along with their out of phase eigen angles as the source of instabilities in the reduced system. The performance of the proposed MOR formulation is tested for perfectly rigid, frequency‐independent, and locally reacting frequency‐dependent boundary conditions in two‐dimensional cases. The study shows that MOR using the stable formulation results in a 100‐fold speedup. The proposed formulation is further evaluated to assess its impact on accuracy, computational speedup, and overall reduction potential of the system.
Key Points
Objective
This work aims to develop a stable model order reduction formulation for time-domain room acoustics simulations.
Methods
- Develops novel structure-preserving formulations for model order reduction.
- Conducts stability analysis to identify eigenvalues causing instabilities.
- Validates the formulation through numerical experiments with various boundary conditions.
Results
- Achieves a 3.5 times speedup in calculating the full-order model compared to unstable methods.
- Demonstrates a 100-fold speedup using the stable formulation.
- Proves improved accuracy and reduction potential in two-dimensional acoustic scenarios.